Graphical timeline from Big Bang to Heat Death

This is the timeline of the Universe from Big Bang to Heat Death scenario. The different eras of the universe are shown. The heat death will occur in 10¹⁰⁰ years, if protons decay.

Usually the logarithmic scale is used for such timelines but it compresses the most interesting Stelliferous Era too much as this example shows. Therefore, a double-logarithmic scale s (s*100 in the graphics) is used instead. The minimum of it is only 1, not 0 as needed, and the negative outputs for inputs smaller than 10 are useless. Therefore, the time from 0.1 to 10 years is collapsed to a single point 0, but that does not matter in this case because nothing special happens in the history of the universe during that time.

s={\begin{cases}\log _{10}\log _{10}year&{\mbox{if }}year>10{\mbox{ , corresponding to }}year=10^{10^{s}}\\0&{\mbox{if }}0.1\leq year\leq 10\\-\log _{10}(-\log _{10}year)&{\mbox{if }}year<0.1{\mbox{ , corresponding to }}year=10^{-10^{-s}}\end{cases}}

Comparison of log₁₀ and log₁₀log₁₀ scales
year	log₁₀ year	combination of log₁₀log₁₀ year and -log₁₀(-log₁₀ year)
10¹⁰⁰⁰⁰	10000	4
10¹⁰⁰⁰	1000	3
10¹⁰⁰	100	2
10¹⁰	10	1
10²	2	0.30
10¹	1	0
10⁰	0	undefined but here forced to 0
10⁻¹	-1	0
10⁻²	-2	-0.30
10⁻¹⁰	-10	-1
10⁻¹⁰⁰	-100	-2

The seconds in the timescale have been converted to years by $second/31557600$ using the Julian year.

References

Fred C. Adams; Greg Laughlin (19 June 2000). The Five Ages of the Universe: Inside the Physics of Eternity. Simon and Schuster. ISBN 978-0-684-86576-8.

See also

References